## Ansari Abdullah ; Ayan Mahalanobis ; Vivek M. Mallick - A new method for solving the elliptic curve discrete logarithm problem

gcc:6649 - journal of Groups, complexity, cryptology, February 16, 2021, Volume 12, Issue 2 - https://doi.org/10.46298/jgcc.2020.12.2.6649
A new method for solving the elliptic curve discrete logarithm problem

Authors: Ansari Abdullah ; Ayan Mahalanobis ; Vivek M. Mallick

The elliptic curve discrete logarithm problem is considered a secure cryptographic primitive. The purpose of this paper is to propose a paradigm shift in attacking the elliptic curve discrete logarithm problem. In this paper, we will argue that initial minors are a viable way to solve this problem. This paper will present necessary algorithms for this attack. We have written a code to verify the conjecture of initial minors using Schur complements. We were able to solve the problem for groups of order up to $2^{50}$.

Volume: Volume 12, Issue 2
Published on: February 16, 2021
Accepted on: February 15, 2021
Submitted on: July 18, 2020
Keywords: Computer Science - Cryptography and Security,Mathematics - Algebraic Geometry,Mathematics - Number Theory